||Earthquake-resistant design in optimizing seismic drift performance presents one of the most challenging engineering problems. Although the research on design optimization of structures has been ongoing for the past few decades, there has been limited effective optimization method for design of building structures subject to seismic drift performance criteria. This research presents a powerful and effective optimal resizing technique, which integrates with the comprehensive time history analysis, for the lateral stiffness design of multi-storey fixed-base and base-isolated concrete building structures under seismic excitations. The optimal seismic drift design problem is formulated as to minimize the cost of building structures subject to lateral drift and element sizing constraints. The optimization methodology developed is based on a rigorously derived Optimality Criteria (OC) method. As an attempt to reduce computational effort, a proper treatment on the point-wise time dependent constraints is needed to eliminate the time parameter in the optimization process. In this regard, a dynamic constraint deletion scheme has been developed to include only the response performance at the critical time steps into the optimal design process. The optimal seismic drift design problem is further extended from fixed-base to base-isolated building structures. Although many research studies have been devoted to the optimal design of base-isolated structures, much effort has been made on the design of either the superstructure or the base isolation system. Therefore, it is intended in this research to simultaneously optimize both the superstructure and the base isolation system as a whole. A major difference and challenge in optimizing a dynamically excited structure versus a statically loaded structure is that the inertia loads and responses change as the dynamic properties of the structure change. Furthermore, multiple local optima may exist in the search for the solution of the design problems. The convergence behaviour of the design optimization process is investigated and an adaptive scaling procedure to overcome the problem is proposed and evaluated. Illustrative examples of both fixed-base and base-isolated structures are presented to demonstrate the efficiency and applicability of the developed optimization technique.